Global analysis of discrete-time SI and SIS epidemic models
Discrete-time SI and SIS models formulated asthe discretization of a continuous-time model may exhibit behaviordifferent from that of the continuous-time model such asperiod-doubling and chaotic behavior unless the step size in the modelis sufficiently small. Some new discrete-time SI andSIS epidemi...
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| Format: | Article |
| Language: | English |
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AIMS Press
2007-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.699 |
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| _version_ | 1832590211664576512 |
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| author | Jianquan Li Zhien Ma Fred Brauer |
| author_facet | Jianquan Li Zhien Ma Fred Brauer |
| author_sort | Jianquan Li |
| collection | DOAJ |
| description | Discrete-time SI and SIS models formulated asthe discretization of a continuous-time model may exhibit behaviordifferent from that of the continuous-time model such asperiod-doubling and chaotic behavior unless the step size in the modelis sufficiently small. Some new discrete-time SI andSIS epidemic models with vital dynamics are formulated and analyzed.These new models do not exhibit period doubling and chaoticbehavior and are thus better approximations to continuous models. However,their reproduction numbers and therefore their asymptotic behavior can differsomewhat from that of the corresponding continuous-time model. |
| format | Article |
| id | doaj-art-bf6ada877fb348a295a60d71ec6217d7 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-bf6ada877fb348a295a60d71ec6217d72025-01-24T01:54:07ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-07-014469971010.3934/mbe.2007.4.699Global analysis of discrete-time SI and SIS epidemic modelsJianquan Li0Zhien Ma1Fred Brauer2Department of Applied Mathematics and Physics, Air Force Engineering University, Xi'an 710051Department of Applied Mathematics and Physics, Air Force Engineering University, Xi'an 710051Department of Applied Mathematics and Physics, Air Force Engineering University, Xi'an 710051Discrete-time SI and SIS models formulated asthe discretization of a continuous-time model may exhibit behaviordifferent from that of the continuous-time model such asperiod-doubling and chaotic behavior unless the step size in the modelis sufficiently small. Some new discrete-time SI andSIS epidemic models with vital dynamics are formulated and analyzed.These new models do not exhibit period doubling and chaoticbehavior and are thus better approximations to continuous models. However,their reproduction numbers and therefore their asymptotic behavior can differsomewhat from that of the corresponding continuous-time model.https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.699discrete-time epidemic modeldynamic behaviorequilibriumstability. |
| spellingShingle | Jianquan Li Zhien Ma Fred Brauer Global analysis of discrete-time SI and SIS epidemic models Mathematical Biosciences and Engineering discrete-time epidemic model dynamic behavior equilibrium stability. |
| title | Global analysis of discrete-time SI and SIS epidemic models |
| title_full | Global analysis of discrete-time SI and SIS epidemic models |
| title_fullStr | Global analysis of discrete-time SI and SIS epidemic models |
| title_full_unstemmed | Global analysis of discrete-time SI and SIS epidemic models |
| title_short | Global analysis of discrete-time SI and SIS epidemic models |
| title_sort | global analysis of discrete time si and sis epidemic models |
| topic | discrete-time epidemic model dynamic behavior equilibrium stability. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.699 |
| work_keys_str_mv | AT jianquanli globalanalysisofdiscretetimesiandsisepidemicmodels AT zhienma globalanalysisofdiscretetimesiandsisepidemicmodels AT fredbrauer globalanalysisofdiscretetimesiandsisepidemicmodels |